Couvreur, Alain Debris-Alazard, Thomas Gaborit, Philippe

In recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network coding or public key cryptography. These applications raised the interest of the community for theoretical properties of this type of codes, such as the hardness of decoding i...

Aamari, Eddie Knop, Alexander

This paper studies the statistical query (SQ) complexity of estimating $d$-dimensional submanifolds in $\mathbb{R}^n$. We propose a purely geometric algorithm called Manifold Propagation, that reduces the problem to three natural geometric routines: projection, tangent space estimation, and point detection. We then provide constructions of these ge...

Marchal, Loris Marette, Thibault Pichon, Grégoire Vivien, Frédéric

Sparse direct solvers using Block Low-Rank compression have been proven efficient to solve problems arising in many real-life applications. Improving those solvers is crucial for being able to 1) solve larger problems and 2) speed up computations. A main characteristic of a sparse direct solver using low-rank compression is when compression is perf...

Gluher, Aude Le Spaenlehauer, Pierre-Jean

We propose a probabilistic variant of Brill-Noether's algorithm for computing a basis of the Riemann-Roch space $L(D)$ associated to a divisor $D$ on a projective nodal plane curve $\mathcal C$ over a sufficiently large perfect field $k$. Our main result shows that this algorithm requires at most $O(\max(\mathrm{deg}(\mathcal C)^{2\omega}, \mathrm{...

Péchoux, Romain

Labbé, Martine Plein, Fränk Schmidt, Martin Thürauf, Johannes

We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow scenarios. We thus analyze ...

Aharonov, Dorit Grilo, Alex B. Liu, Yupan

StoqMA characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem. Although error reduction is commonplace for many complexity classes, such as BPP, BQP, MA, QMA, etc.,this property remains open for StoqMA since Bravyi, Bessen and Terhal defined this class ...

Baillot, Patrick Ghyselen, Alexis

Type systems as a technique to analyse or control programs have been extensively studied for functional programming languages. In particular some systems allow to extract from a typing derivation a complexity bound on the program. We explore how to extend such results to parallel complexity in the setting of the pi-calculus, considered as a communi...

Neiger, Vincent Pernet, Clément

This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, to our knowledge, this was only achieved by resorting to genericity assumptions or randomization techniques, while the best k...

Alves, Thomas Rivière, Jérémy ALAUX, Cédric Le Conte, Yves Singhoff, Frank Duval, Thierry Rodin, Vincent

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